Harvard 1940–1941: Tarski, Carnap and Quine on a finitistic language of mathematics for science

Tarski, Carnap and Quine spent the academic year 1940–1941 together at Harvard. In their autobiographies, both Carnap and Quine highlight the importance of the conversations that took place among them during the year. These conversations centred around semantical issues related to the analytic/synthetic distinction and on the project of a finitist/nominalist construction of mathematics and science. Carnap's Nachlaß in Pittsburgh contains a set of detailed notes, amounting to more than 80 typescripted pages, taken by Carnap while these discussions were taking place. In my article, I present a survey of these notes with special emphasis on Tarski's rejection of the analytic/synthetic distinction, the passage from typed languages to first-order languages, Tarski's finitism/nominalism, and the construction of a finitist language for mathematics and science.

[1]  Nelson Goodman,et al.  Steps toward a constructive nominalism , 1947, Journal of Symbolic Logic.

[2]  S. Feferman.  Comments on “Predicativity as a philosophical position” by G. Hellman , 2004, Revue internationale de philosophie.

[3]  Jan Woleński,et al.  On Tarski’s Background , 1995 .

[4]  Jan Woleński,et al.  Logic and philosophy in the Lvov-Warsaw school , 1988 .

[5]  Jack Kaminsky.  The Philosophy of W. V. Quine , 1987 .

[6]  G. Hellman.  Comments on " Predicativity as a Philosophical Position " , 2004 .

[7]  José Ferreirós Domínguez.  Notes on types, sets, and logicism, 1930-1950 , 1997 .

[8]  Solomon Feferman,et al.  Alfred Tarski: Life and Logic , 2004 .

[9]  Thomas Uebel,et al.  Dear Carnap, Dear Van: The Quine-Carnap Correspondence and Related Work , 1995 .

[10]  Paolo Mancosu,et al.  Mathematical Explanation: Problems and Prospects , 2001 .

[11]  Christina Alm-Arvius,et al.  Introduction to Semantics , 1997 .

[12]  Willard Van Orman Quine,et al.  Designation and Existence , 1939 .

[13]  Henry S. Leonard,et al.  Testability and Meaning. , 1937 .

[14]  José Ferreirós,et al.  The Road to Modern Logic—An Interpretation , 2001, Bulletin of Symbolic Logic.

[15]  A. Fraenkel.  Untersuchungen über die Grundlagen der Mengenlehre , 1925 .

[16]  D. Hilbert.  Die grundlagen der mathematik , 1928 .

[17]  Alfred Tarski.  Drei Briefe an Otto Neurath , 1992 .

[18]  E. Zermelo.  Über Grenzzahlen und Mengenbereiche , 1930 .

[19]  Willard Van Orman Quine,et al.  The time of my life : an autobiography , 1988 .

[20]  Paolo Mancosu.  Tarski on models and logical consequence , 2006 .

[21]  Alfred Tarski.  Pojęcie prawdy w językach nauk dedukcyjnych , 1933 .

[22]  Alfred Tarski,et al.  Der Wahrheitsbegriff in den formalisierten Sprachen , 1935 .

[23]  A. Tarski,et al.  What are logical notions , 1986 .

[24]  Solomon Feferman,et al.  Why a Little Bit Goes a Long Way: Logical Foundations of Scientifically Applicable Mathematics , 1992, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association.

[25]  M. White,et al.  A Philosophical Letter of Alfred Tarski , 1987 .

[26]  Rudolf Haller,et al.  Alfred Tarski: Drei Briefe an Otto Neurath , 1992 .